The Dutch international midfielder has signed a five-year contract with the option of a sixth year.
United will pay €39m up-front for Van de Beek with a further €5m in add-ons.
Van de Beek, 23, has risen to prominence as part of the impressive Ajax side in recent years.
VDB: “A club with amazing history”
Van de Beek spoke of his great excitement at joining the Red Devils.
“I cannot begin to explain how incredible an opportunity it is to join a club with such an amazing history,” he said. “I would like to thank everyone at Ajax. I grew up there and I will always have a special bond with the club.
“I am now ready to take the next step in my career and perform at the highest level and there is no higher standard than Manchester United.
“Everyone has told me how amazing the Old Trafford atmosphere is and I am looking forward to experiencing that, once it is safe for the fans to return.
“This team has some of the best midfielders in the world and I know that I can learn from them and also bring my own strengths to the group.
“Having spoken to the manager about his vision for this team, the direction that the club is going in is hugely exciting and I cannot wait to be a part of that.”
Ole Gunnar Solskjaer reported played a big role in luring Van de Beek to Old Trafford. And the United boss is sure the midfielder will succeed in his team.
Solskjaer said: “Donny has all of the technical attributes needed to perform in this team and has the personality required to succeed at Manchester United.
“His ability to see space, time his movements and read the game will really complement the qualities that we have in midfield and his arrival really strengthens the depth of talent we have in that position.
“Donny’s performances in the Eredivisie and in Europe have been excellent over the last few years and we are all looking forward to working with him.”
Van de Beek leaves Ajax after making 175 appearances, in which he scored 41 and assisted 34 assists.